Question: Multiply the following complex numbers, marked as blue dots on the graph: $(1) \cdot (6 e^{5\pi i / 4})$ (Your current answer will be plotted in orange.)
Solution: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $1$ ) has angle $0$ and radius $1$ The second number ( $6 e^{5\pi i / 4}$ ) has angle $\frac{5}{4}\pi$ and radius $6$ The radius of the result will be $1 \cdot 6$ , which is $6$ The angle of the result is $0 + \frac{5}{4}\pi = \frac{5}{4}\pi$ The radius of the result is $6$ and the angle of the result is $\frac{5}{4}\pi$.